Bohpier: Difference between revisions

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'''Bohpier temperament''' is a rank-two temperament for 7, 11, and 13 [[Harmonic limit|prime limits]]. It tempers out 100/99, 144/143, 196/195, and 275/273 in the 13-limit, as well as the [[245/243|sensamagic comma]] (245/243) and the gariboh comma (3125/3087). It is strongly related to [[Bohlen-Pierce]] scale, and from this it derives its name. Generator for the bohpier can be used either [[13edt|13ED3]], [[19ed5|19ED5]], or [[23ed7|23ED7]]. [[41edo|41EDO]] is an excellent tuning for the bohpier, with generator 5\41, and MOS of 8, 9, 17, 25, or 33 notes are available.

'''Bohpier temperament''' is a rank-two temperament for 7, 11, and 13 [[Harmonic limit|prime limits]]. It is a member of [[Sensamagic clan|sensamagic]], [[Gariboh clan|gariboh]], [[Arcturus clan|arcturus]], and [[Mirkwai clan|mirkwai]] temperaments. It tempers out 100/99, 144/143, 196/195, and 275/273 in the 13-limit, as well as the [[245/243|sensamagic comma]] (245/243) and the gariboh comma (3125/3087). It is strongly related to [[Bohlen-Pierce]] scale, and from this it derives its name. Generator for the bohpier can be used either [[13edt|13ED3]], [[19ed5|19ED5]], or [[23ed7|23ED7]]. [[41edo|41EDO]] is an excellent tuning for the bohpier, with generator 5\41, and MOS of 8, 9, 17, 25, or 33 notes are available.

~~See~~ [[~~Sensamagic clan #Bohpier~~]] ~~for more technical data~~.

== Temperament data ==

<div style="line-height:1.6;">'''Bohpier Temperament (8d & 41)'''</div>

Subgroup: 2.3.5.7.11.13

[[Comma list]]: 100/99, 144/143, 196/195, 275/273

[[Mapping]]: [{{val| 1 0 0 0 2 2 }}, {{val| 0 13 19 23 12 14 }}]

[[POTE generator]]:

* 7-limit: ~27/25 = 146.47407

* 11-limit: ~12/11 = 146.54458

* 13-limit: ~12/11 = 146.60266

[[TOP tuning|TOP generator]]s:

* 7-limit: ~2 = 1200.00000, ~27/25 = 146.47407

* 11-limit: ~2 = 1199.23623, ~12/11 = 146.45131

* 13-limit: ~2 = 1198.55643, ~12/11 = 146.42630

[[Diamond monotone]] ranges:

* 5-odd-limit: ~27/25 = [144.00000, 150.00000] (3\25 to 1\8)

* 7-odd-limit: ~27/25 = [145.45455, 150.00000] (4\33 to 1\8)

* 9, 11, and 13-odd-limit: ~12/11 = [145.45455, 146.93878] (4\33 to 6\49)

* 15-odd-limit: ~12/11 = [146.34146, 146.93878] (5\41 to 6\49)

[[Diamond tradeoff]] ranges:

* 5-odd-limit: ~27/25 = [146.30423, 147.39312]

* 7-odd-limit: ~27/25 = [145.62805, 147.39312]

* 9 and 11-odd-limit: ~12/11 = [145.02803, 147.39312]

* 13 and 15-odd-limit: ~12/11 = [138.57266, 150.63706]

Diamond monotone and tradeoff ranges:

* 5-odd-limit: ~27/25 = [146.30423, 147.39312]

* 7-odd-limit: ~27/25 = [145.62805, 147.39312]

* 9, 11, and 13-odd-limit: ~12/11 = [145.45455, 146.93878]

* 15-odd-limit: ~12/11 = [146.34146, 146.93878]

[[Optimal GPV sequence]]s:

* 7-limit: {{Vals| 41, 131, 172, 213c }}

* 11-limit: {{Vals| 41, 90e, 131e }}

* 13-limit: {{Vals| 41, 90ef, 131ef, 221bdeff }}

[[Badness]]:

* 7-limit: 0.068237

* 11-limit: 0.033949

* 13-limit: 0.024864

</div></div>

== Intervals ==

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-'''Bohpier temperament''' is a rank-two temperament for 7, 11, and 13 [[Harmonic limit|prime limits]]. It tempers out 100/99, 144/143, 196/195, and 275/273 in the 13-limit, as well as the [[245/243|sensamagic comma]] (245/243) and the gariboh comma (3125/3087). It is strongly related to [[Bohlen-Pierce]] scale, and from this it derives its name. Generator for the bohpier can be used either [[13edt|13ED3]], [[19ed5|19ED5]], or [[23ed7|23ED7]]. [[41edo|41EDO]] is an excellent tuning for the bohpier, with generator 5\41, and MOS of 8, 9, 17, 25, or 33 notes are available.
+'''Bohpier temperament''' is a rank-two temperament for 7, 11, and 13 [[Harmonic limit|prime limits]]. It is a member of [[Sensamagic clan|sensamagic]], [[Gariboh clan|gariboh]], [[Arcturus clan|arcturus]], and [[Mirkwai clan|mirkwai]] temperaments. It tempers out 100/99, 144/143, 196/195, and 275/273 in the 13-limit, as well as the [[245/243|sensamagic comma]] (245/243) and the gariboh comma (3125/3087). It is strongly related to [[Bohlen-Pierce]] scale, and from this it derives its name. Generator for the bohpier can be used either [[13edt|13ED3]], [[19ed5|19ED5]], or [[23ed7|23ED7]]. [[41edo|41EDO]] is an excellent tuning for the bohpier, with generator 5\41, and MOS of 8, 9, 17, 25, or 33 notes are available.
-See [[Sensamagic clan #Bohpier]] for more technical data.
+== Temperament data ==
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">'''Bohpier Temperament (8d &amp; 41)'''</div>
+<div class="mw-collapsible-content">
+Subgroup: 2.3.5.7.11.13
+[[Comma list]]: 100/99, 144/143, 196/195, 275/273
+[[Mapping]]: [{{val| 1 0 0 0 2 2 }}, {{val| 0 13 19 23 12 14 }}]
+[[POTE generator]]:
+* 7-limit: ~27/25 = 146.47407
+* 11-limit: ~12/11 = 146.54458
+* 13-limit: ~12/11 = 146.60266
+[[TOP tuning|TOP generator]]s:
+* 7-limit: ~2 = 1200.00000, ~27/25 = 146.47407
+* 11-limit: ~2 = 1199.23623, ~12/11 = 146.45131
+* 13-limit: ~2 = 1198.55643, ~12/11 = 146.42630
+[[Diamond monotone]] ranges:
+* 5-odd-limit: ~27/25 = [144.00000, 150.00000] (3\25 to 1\8)
+* 7-odd-limit: ~27/25 = [145.45455, 150.00000] (4\33 to 1\8)
+* 9, 11, and 13-odd-limit: ~12/11 = [145.45455, 146.93878] (4\33 to 6\49)
+* 15-odd-limit: ~12/11 = [146.34146, 146.93878] (5\41 to 6\49)
+[[Diamond tradeoff]] ranges:
+* 5-odd-limit: ~27/25 = [146.30423, 147.39312]
+* 7-odd-limit: ~27/25 = [145.62805, 147.39312]
+* 9 and 11-odd-limit: ~12/11 = [145.02803, 147.39312]
+* 13 and 15-odd-limit: ~12/11 = [138.57266, 150.63706]
+Diamond monotone and tradeoff ranges:
+* 5-odd-limit: ~27/25 = [146.30423, 147.39312]
+* 7-odd-limit: ~27/25 = [145.62805, 147.39312]
+* 9, 11, and 13-odd-limit: ~12/11 = [145.45455, 146.93878]
+* 15-odd-limit: ~12/11 = [146.34146, 146.93878]
+[[Optimal GPV sequence]]s:
+* 7-limit: {{Vals| 41, 131, 172, 213c }}
+* 11-limit: {{Vals| 41, 90e, 131e }}
+* 13-limit: {{Vals| 41, 90ef, 131ef, 221bdeff }}
+[[Badness]]:
+* 7-limit: 0.068237
+* 11-limit: 0.033949
+* 13-limit: 0.024864
+</div></div>
 == Intervals ==